Abstract
Suppose thatG is a compact Lie group and that Γ denotes a maximal set of inequivalent irreducible unitary continuous representations ofG. In a recent paperCecchini showed that a necessary (and sufficient) condition for\(E \subseteq \Gamma \) to be a local central Λ(4) set is that sup{d(γ)∶γ∈E}<∞, whered(γ) is the dimension of γ. The main result below is thatevery subset of Γ is local central Λ (2). In addition, whenG isU(n) orSU(n), n≥2, it is shown that every subset of Γ is local central Λ(p) for allp<2+2/n. An example ofRider shows that this is best possible.
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Price, J.F. On local central lacunary sets for compact Lie groups. Monatshefte für Mathematik 80, 201–204 (1975). https://doi.org/10.1007/BF01319915
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DOI: https://doi.org/10.1007/BF01319915